Table 9 Evaluation metrics.
From: Hydropower station scheduling with ship arrival prediction and energy storage
Performance metrics | Optimal value | Mathematical formula |
|---|---|---|
MSE: Evaluates the degree of variability of the data. The smaller the value, the better the accuracy of the model | 0 | \(MSE=\frac{1}{n} \sum _{i=1}^{T}\left( \widehat{y_{i} } - y_{i} \right) ^{2}\) |
MAE: The average distance between the model predicted value and the sample true value | 0 | \(MAE = \frac{1}{n}\sum _{i=1}^{n} \left| \widehat{y_{i} } -y_{i}\right|\) |
RMSE: Evaluate the deviation between observed and actual values. The smaller the value, the better the prediction | 0 | \(RMSE = \sqrt{\frac{1}{n}\sum _{i=1}^{n}(\widehat{y_{i} } - y_{i})^{2}}\) |
MAPE: Statistical indicator used to measure prediction accuracy, 0% indicates a perfect model, greater than 100% indicates a poor model | 0 | \(MAPE = \frac{100\%}{n}\sum _{i=1}^{n} \left| \frac{\widehat{y_{i} }- y_{i}}{y_{i}}\right|\) |
\(R^{2}\): A quantity used to measure how well the model fits. The scale interval is [0,1]. The closer to 1, the better the model fit | 1 | \(R^{2} =1-\frac{\sum _{i=1}^{n}(\widehat{y_{i}} -y_{i} )^{2}}{\sum _{i=1}^{n}(y_{i}-\overline{y})^{2}}\) |
